! Cassidy Morgan Tits !

1608 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 4, JULY 2014

Optimal Bidding Strategy for Microgrids ConsideringRenewable Energy and Building Thermal Dynamics

Duong Tung Nguyen and Long Bao Le, Senior Member, IEEE

Abstract—In this paper, we study an optimal day-ahead price-based power scheduling problem for a community-scale microgrid(MG). The proposed optimization framework aims to balance be-tweenmaximizing the expectedbenefit of theMGin thederegulatedelectricity market and minimizing the MG operation cost consid-ering users’ thermal comfort requirements and other system con-straints. The power scheduling and bidding problem is formulatedas a two-stage stochastic programwhere various system uncertain-ties are captured by using the Monte Carlo simulation approach.Our formulation is novel in that it can exploit the thermal dynamiccharacteristics of buildings to compensate for the variable and in-termittent nature of renewable energy resources and enables us toachieve desirable tradeoffs for different conflicting design objec-tives. Extensive numerical results are presented to demonstrate thegreat benefits in exploiting the building thermal dynamics and theflexibility of the proposed scheduling method in achieving differentpractical design tradeoffs. We also investigate the impacts of dif-ferent design and system parameters on the curtailment of renew-able energy resources and the optimal expected profit of the MG.

Index Terms—Building thermal dynamics, climate comfort re-quirement, day-ahead market, optimal biding strategy.

NOMENCLATURE

Duration of time slot (h).

Maximum allowable temperature deviation.

Coefficient of performance of HVACsystem in building .

Conversion coefficient of solar unit (%).

Charging/discharging efficiency of battery.

Solar irradiance .

Cost of temperature deviation .

Cost of bid deviation ($/kWh).

Probability of scenario .

“1” for cooling, “ 1” for heating.

Manuscript received August 05, 2013; revised November 08, 2013 and Jan-uary 22, 2014; accepted March 22, 2014. Date of current version June 18, 2014.Paper no. TSG-00606-2013.The authors are with Institut National de la Recherche Scientifique-Énergie,

Matériaux et Télécommunications (INRS-EMT), Université du Québec, Mon-tréal, QC H2X 1L7, Canada (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2014.2313612

Binary variable, “1” if charging/discharging.

Production cost of unit ($).

Cost for battery degradation ($/kWh).

Shutdown/startup offer cost of unit ($).

Ramping-down/up rate limit of unit (kW).

Minimum down/up time of unit (h).

Capacity of battery (kWh).

Minimum/maximum energy stored inbattery (kWh).

Day-ahead and real-time prices ($/kWh).

Energy stored in battery (kWh).

Indices of conventional unit, wind unit,solar unit, building, battery, time slot, andscenario.

Commitment status of unit at time .

Total non-HVAC load (kW).

Maximum loss of load percentage at time .

Realized and maximum load shedding(kW).

Index of segment and number of segmentsof piecewise linear cost function of unit .

Number of buildings/scenarios/time slots.

Number of conventional/battery units.

Number of wind/solar units.

Minimum/maximum power generation ofunit (kW).

Rated power of HVAC system (kW).

Scheduled day-ahead bid and actualreal-time power delivery (kW).

Rated power of wind unit (kW).

Power generation of unit (kW).

Power generation of unit from the -thsegment at time in scenario (kW).

Output power of HVAC system (kW).

1949-3053 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

NGUYEN AND LE: OPTIMAL BIDDING STRATEGY FOR MICROGRIDS 1609

Input power supplied to HVAC system(kW).

Charging/discharging power of battery(kW).

Maximum charging/discharging power(kW).

Wind/solar power curtailment (kW).

Wind/solar available output power (kW).

Array area of solar unit .

Shutdown/startup cost of unit ($).

Desired indoor temperature of building.

Indoor temperature of building j andoutdoor temperature at time in scenario

.

Cost of renewable energy curtailment($/kWh).

Wind speed at time in scenario (m/s).

Cost of wind/solar/load curtailment($/kWh).

Rated, cut-in, and cut-out wind speed(m/s).

Startup and shutdown indicators {0,1}.

LSF Load scaling factor.

USF Uncertainty scaling factor.

I. INTRODUCTION

T HE intermittent and volatile nature of renewable energygeneration imposes a significant challenge to integrate

these resources into power systems. Various methods havebeen proposed to tackle the intermittency and volatility ofrenewable energy resources. In [1]–[4], the authors proposed touse pumped-storage hydro units coordinated with wind sourcesto maximize the profits of generation companies (GENCOs),or to minimize the operating costs for power system operators.The optimal battery sizing problem was studied in [5], [6] tocope with the uncertainties in renewable energy generation. Thepotential of using charging/discharging capability of electricvehicles (EVs) to support renewable energy was investigatedin [7], [8]. Other technologies such as compressed air storage[9], fast-response units (e.g., gas-fired units) [10] can also beused to mitigate the fluctuation of renewable energy gener-ation. However, these solutions have some drawbacks, e.g.,pumped-storage hydro systems are geographically dependentand it takes a long time to build a pumped-storage facility witha high capital cost.Another important issue in future smart grids is intelligent

demand side management (DSM) by taking advantages oftime-varying electricity prices. In this paper, we consider thesmart DSM of the heating, ventilation, and air-conditioning(HVAC) system. There have been several proposed optimal

control schemes for HVAC systems to minimize their opera-tion costs considering different temperature comfort criteria[11]–[15]. Users typically desire to maintain the indoor tem-perature at their preferred setpoint, which depends on users’preferences and building occupancy status [12]. In general,users can tolerate a small deviation of the indoor temperaturefrom the desired setpoint. Obviously, users would feel morecomfortable when the indoor temperature is closer to the pre-ferred setpoint. If the desirable temperature and the maximumallowable temperature deviation are given then the indoor tem-perature should be maintained to be in the temperature comfortrange. Then, the HVAC power consumption can be scheduledintelligently to achieve electricity cost saving without violatingusers’ comfort requirements. In particular, the HVAC systemcan consume more power during low-priced hours to precool(preheat) buildings in the summer (winter) while it can reducethe power consumption during high-priced hours while stillmaintaining indoor temperature in the comfort zone thanks tothe building thermal inertia.In this paper, we not only consider electricity price variation

in scheduling HVAC power consumption, but we also proposeto exploit the thermal dynamic characteristics of buildings (e.g.,campus, residential or office buildings) to accommodate the un-certainties in renewable energy generation. In the U.S., build-ings contribute for a significant fraction of the overall powerconsumption; moreover, thermal load accounts for about 50%of the total load in buildings [16]. Therefore, the high thermalstorage capacity of buildings could make the HVAC systema great candidate in solving the renewable energy integrationproblem. The idea is that HVAC power consumption can bescheduled according to the renewable energy generation profile,e.g., when the renewable power is higher than expected, HVACsystemsmay consumemore power to precool/preheat buildings,and vice versa. The potential of the thermal storage capabilityof buildings is assessed in a MG setting where the consideredMG participates in a deregulated electricity market with the ob-jective of maximizing its expected profit (i.e., revenue minusoperation cost).Optimal bidding strategies for participants in power markets

have been extensively studied in the literature. The majorityof existing works has focused on optimizing the operationof generators in the supply side to maximize the profits ofGENCOs [1]–[4], [17]–[23]. In addition to GENCOs, thereare other important entities such as distribution companies(DISCOs), retail companies (RETAILCOs), aggregators [23]that can participate in the deregulated electricity market wherethese entities can be considered belonging to the demand side(e.g., buying electricity from the wholesale market to servecustomers). In [24]–[28], different operation frameworks forDISCOs, RETAILERs, and larger customers in the competitiveelectricity market have been proposed. In [29], [30], the authorsstudied the optimal energy trading problem for an aggregatorthat controls the operation of a number of EVs.In this work, we consider a particular market entity which is

a MG aggregator. In general, a MG can be defined as a clusterof distributed energy resources (DERs) and associated loads,and it can be operated in grid-connected mode or islanded mode[31]. A MG can be of different sizes ranging from a building,a university campus, to the community scale (e.g., a village).


Capacities of DERs in a MG can be relatively small to allowthem participate directly in the power market. Therefore, localelectricity generation and demand in the MG can be aggregatedand controlled by a MG aggregator which serves as the repre-sentative of the MG in the market. Moreover, the MG can beconsidered as a “prosumer” which not only consumes but alsoproduces electricity [32]. Particularly, when the local genera-tion is higher than the local demand, the MG acts as a producerselling its surplus energy to the main grid. In contrast, when thelocal generation is not sufficient to meet the local demand, theMG plays the role of a consumer who buys electricity from themarket to serve its local demand. In this work, we assume thatthe MG is allowed to participate in the electricity market andthe market operator treats the MG the same manner as othermarket entities (e.g., GENCOs and DISCOs). From the marketoperator’s perspective, the MG can act either as a supplier or acustomer depending on the direction of power flow between theMG and the main grid.There is an important difference between MGs and GENCOs

in that the supply-demand balancing constraint does not exist inthe power scheduling problem for GENCOs. On the other hand,supply-demand balance is a critical requirement in the powerscheduling and bidding problem for MGs. Moreover, the de-mand response can be integrated in the power scheduling op-timization for MGs, which can potentially reduce considerablythe operating cost for MGs and compensate for the fluctuationof RESs. Optimal energy trading for MGs has been consid-ered in several studies [31], [33]–[44] where the typical objec-tives of these works are to maximize the revenue for the MG inthe power market and to minimize the MG operation cost. Ourcurrent work belongs to this line of research, which, however,has several distinct modeling aspects. To best of our knowl-edge, there is no existing work considering a detailed modelfor building thermal dynamics and the potential of using HVACsystems and the associated thermal load to cope with the uncer-tainties of RESs and maximize the profit for MGs in the elec-tricity market. Our work fills this important gap in the literaturewhere its main contributions can be summarized as follows:• We propose a comprehensive model based on which wedevelop an optimal day-ahead scheduling strategy for aMG in a two-settlement electricity market, which is thecommon practice in the U.S. [3], [22], [23]. The proposedmodel aims to balance between maximizing the revenuefor the MG and minimizing the load and renewable cur-tailment as well as bid deviation while maintaining users’comfort requirements and other system constraints. Theproposed model is novel in that it enables us to exploit thebuilding thermal dynamics properties to compensate forthe variability of renewable energy generation, which cansignificantly improve the MG profit. Specifically, HVACload is used as a demand response source and integratedinto the optimal bidding strategy of the MG aggregator inthe electricity market.

• The optimization model is formulated as a two-stage sto-chastic programming problem where uncertainties are cap-tured by using the Monte Carlo simulation method. First-stage and second-stage variables are appropriately definedfor efficient operations of the power systems integratingdifferent renewable energy sources.

• We present extensive simulation results to demonstrate theadvantages in coordinating the operations of the HVACsystems and renewable energy resources compared tothe uncoordinated case where HVAC systems and othercomponents of the MG aim to optimize their power con-sumption/generation independently. The performance ofthe proposed scheme is also compared with that under thestrict climate comfort requirement where no temperaturedeviation is allowed. Finally, the sensitivity analysis isperformed to assess the impacts of different system anddesign parameters on the optimal solution.

The remaining of this paper is organized as follows. Thesystem model and modeling approach are presented in Sec-tion II. Detailed problem formulation is described in Section III.The case studies and numerical results are provided in Section Vfollowed by conclusion in Section VI.

II. SYSTEM MODEL AND MODELING APPROACH

A. System Model

1) MGComponents: We consider a large-scale MG that con-sists of several renewable generating units, conventional units,a number of buildings with associated loads, and an optionalbattery storage facility. The renewable generating units includesolar panels and wind turbines. In this study, conventional gen-erating units refer to non-renewable generating units such as mi-croturbines, fuel cells, diesel generators.1 The MG loads are di-vided into two separate types, namely HVAC and non-HVACloads. In reality, this kind of MG is very popular (e.g., energycooperative model [45]).In general, the MG aggregator desires to maximize the uti-

lization of renewable energy generation. The shortened and ex-cess amount of energy required to balance the local load can beaccommodated by trading with the main grid through the Pointof Common Coupling (PCC) [31] or by running conventionalunits. The MG aggregator will make decisions on purchasingelectricity from the market or running local conventional unitsdepending on various factors such as electricity price, the statesof conventional units, and the marginal cost of operating con-ventional units. We consider the energy scheduling and bid-ding problem for MG in discrete time slots, denoted by in ourmodel, over a scheduling period of NH time slots.2) HVACOperation: HVAC systems are typically controlled

by the thermostats to maintain indoor temperature at preferredsetpoints. Users can choose desirable temperature setpoints fordifferent occupancy statuses (e.g., being at home, away, andslipping). As discused in Section I, users would feel the mostcomfortable if the indoor temperature is at the preferred set-point. However, they can tolerate a certain small deviation ofthe indoor temperature from the setpoint. The larger the devia-tion is, the less comfortable users would feel. In this work, weassume that the indoor temperature must be maintained to be inthe comfort range (e.g., [21 , 25 ]).Moreover, indoor temperature in a particular time slot de-

pends on the amount of scheduled power and the temperaturein the previous time slot due to building thermal inertia. There-fore, it would be beneficial if the HVAC system consumes moreenergy when the electricity price is low or when the amount

1In reality, conventional units are often refereed to as thermal generators.


of generated renewable energy is high to precool or preheatbuildings (for the summer and winter, respectively) and reducethe power consumption in opposite cases. Thus, the HVACpower consumption should be scheduled economically whilemaintaining the indoor temperature within the required comfortrange. By allowing the MG aggregator to control the operationof HVAC systems in their buildings, significant cost savingmay be achieved based on which users of the MG could receivesome saving in their electricity bills.3) Market Model: The MG is assumed to be a price-taker

in the electricity market. During the time slots where the localpower generation is surplus, the MG would sell its power to themain grid. In contrast, if the local generation is not enough tomeet its local load, the MG would need to buy electricity fromthe main grid. Everyday the MG has to submit its hourly bidsto the day-ahead market several hours before physical powerdelivery [2]. The MG bids include both selling and buying elec-tricity bids. Also, the MG can participate in the real-time elec-tricity market to supplement for any power deviation from theday-ahead schedule. It is the common practice that the MGoffers selling bids at a very low price (e.g, normally set to 0$/MWh [2], [3], [46]) and buying bids at high prices to en-sure that its submitted bids are always accepted in the market.The market operator is responsible for calculating the marketclearing prices after collecting all offer bids and demand bidsfrom all competitive entities in the market [23], [46]. The pay-ment made between the MG and the market operator is calcu-lated based on the market clearing prices.Finding an optimal hourly bidding strategy for the MG is

a challenging task due to various uncertainties in the system,which may cause a significant deviation between the scheduledpower delivery and the real-time power delivery. If the MGcannot follow the day-ahead scheduled power, a penalty will beapplied to the bid deviation [1]–[4], [22]. When the available re-newable output power is higher than scheduled, it is sometimespreferable to curtail the surplus renewable power to avoid a highpenalty cost on the bid deviation. The thermal storage capabilityof buildings can help mitigate the affects of renewable energyuncertainties by increasing HVAC power consumption when re-newable energy generation is higher than scheduled, and viceversa. By exploiting this aspect in HVAC power scheduling, itis, therefore, expected that the real-time power delivery will becloser to the day-ahead schedule, and the renewable energy cur-tailment is reduced.

B. Stochastic-Based Optimization Approach

There are various sources of uncertainties in our proposedmodel, which arise from the renewable energy generation,the total non-HVAC load, the ambient temperature, and theday-ahead and real-time electricity prices. The Monte Carlosimulation is used to generate scenarios that represent theseuncertain parameters based on the corresponding distributionfunctions [1]–[4], [6]–[8], [47]–[49]. In general, the largerthe number of scenarios we generate, the more accurate theoptimal solution can be achieved. However, there is a trade-offbetween the number of simulated scenarios and the computa-tional burden of the scenario-based optimization method. For alarge-scale problem, suitable scenario reduction techniques canbe employed to reduce the number of scenarios, consequently,reduce the computational burden [47], [50].

III. PROBLEM FORMULATION

The power scheduling and bidding problem is formulated asa two-stage stochastic program. The inputs to the underlyingproblem include Monte Carlo scenarios which represent theuncertainties in renewable output power (wind and solar), totalnon-HVAC load of all buildings, ambient temperature, and elec-tricityprice information.Theoutputsof theoptimizationproblemconsist of the sets offirst-stagedecisions and the second-stagede-cisions. Thedecisions taken at thefirst stagemust bemadebeforeuncertainties are disclosed considering possible realizations ofuncertain parameters at the second stage. The recourse decisionsat the second-stage are made after the uncertainties are unveiled,and they depend on the first-stage decisions.In this paper, the first-stage decisions include the commitment

statuses of all conventional units and the hourly bid quantitiessubmitted to the day-ahead market. The second-stage decisionsinclude the power dispatch of all generating units, the amount ofinvoluntary load curtailment, the real-time power delivery be-tween the MG and the main grid, and the battery charging/dis-charging decisions. In the following, all the second-stage deci-sion variables are denoted with a superscript representing sce-nario . The stochastic problem in the joint optimization case isdescribed as follows.

A. Objective Function

Our design goal is to maximize the following objective func-tion.

(1)

where is the hourly bid that the MG submits to the day-aheadmarket, is the real-time power delivery. The mismatch be-tween the scheduled day-ahead power and the actual power de-livery is indeed the amount of power that the MGtrades in the real-time market. A positive value of meansthat the power is exported from the MG to the main grid andvice versa. The same convention is applied to and .The proposed objective function represents the expected

profit of the MG which is equal to the expected revenue at-tained by trading in both day-ahead and balancing marketsminus the MG operating cost. The expected revenue of the MGis

(2)


In fact, if is positive (negative) then the termrepresents the revenue (cost) of theMG by selling (buying) elec-tricity in the day-ahead market in time . Similarly, ifis positive (negative) then the term describesthe revenue (cost) of the MG by selling (buying) electricity inthe real-time market in time slot and scenario . The term

presents the penalty imposed on the MG ag-gregator in time slot and scenario when the actual real-time power delivery is different from the scheduled day-aheadvalue [22].The MG operating cost consists of the startup cost, the

shutdown cost, the operating cost of conventional units, andother costs including users’ temperature discomfort cost,battery degradation cost, penalties due to wind/solar energycurtailment, and involuntary load curtailment. In particular, thetotal startup cost and the shutdown cost for conventional unitsover the scheduling horizon is expressed in the first term in(1) while the second term in (1) presents the operating cost ofconventional units.The third term in (1) represents the penalty due to temperature

deviations in buildings. Specifically, de-scribes the temperature discomfort cost for residents of buildingin time slot and scenario . The parameter represents

the willingness of residents of building to trade their climatecomfort for cost saving in time slot . The larger is, the lesswilling the residents in building are, which results in less flexi-bility in scheduling power consumption of the HVAC system ofbuilding . Here, can be interpreted as thepayment that the MG aggregator pays the residents of buildingin time slot and scenario for their participation in the un-derlying control scheme.The term captures the degra-

dation cost for battery in time slot and scenario due tocharging/discharging activities [7], [17], [51], [52]. In addition,the penalty for curtailment of involuntary load is proportionalto the amount of load shedding. To ensure a high quality ofservice for users, involuntary load curtailment needs to beavoided, hence should be set to a very high value. Fi-nally, the last two terms in (1) represent the penalty for windand solar energy curtailment, respectively. Renewable energycurtailment penalty is employed to account for the benefitsassociated with renewable energy that have not been includedexplicitly in the existing model (e.g., subsides from governmentto encourage increasing renewable energy penetration, carbonemissions reduction, and Renewable Energy Certificate (REC)policy) [49], [53]. We propose to include the renewable energycurtailment penalty in the objective function to increase theflexibility of the proposed model, which provides the MGaggregator the mechanism to efficiently control the amount ofcurtailment2. In general, the higher values of weighting factors

and/or results in a lower amount of renewable energy

2In many cases, penalty for renewable energy curtailment (or, also the dis-comfort cost) might not have actual economic values (e.g., there is no subsidepolicies for renewable energy, no REC policy, etc or users do not receive theexact amount of discomfort cost as modeled in (1)), we might still want to putthe terms representing those penalties in the objective function with the purposeof allowing the MG aggregator more flexibly in controlling the amount of re-newable energy curtailment, and users discomfort. However, the cost for thosepenalties will not be included in the real cost (or profit) value for the MG ag-gregator.

curtailment. Other constraints of the optimization problem aredescribed in the following.

B. Power Balance

For each scenario , the sum of the total power generationfrom all local generating units, the amount of involuntary loadcurtailment, and the charging/discharging power of battery unitsmust be equal to the sum of the real-time power delivery, HVACand non-HVAC loads. Note that and are the max-imum available wind power and the amount of wind power cur-tailment at time in scenario , respectively. The difference be-tween them is the actual wind power generation at time in sce-nario . Similar explanation is applied to solar power genera-tion. The power balance equation for each time and scenariois given as follows:

(3)

C. Power Exchange With Main Grid

We can impose a limit on the quantity of power submittedto the day-ahead market as well as the amount of real-timepower delivery. Let be the maximum allowable powerexchange between the MG and the main grid then we have

(4)

D. Constraints for Conventional Units

The operating cost of conventional unit can be modeled ap-proximately by a piecewise linear function as follows [49], [54]:

(5)

(6)

(7)

where is number of segments of energy production curvefor unit and is the marginal cost of the segmentoffered by unit in time slot ($/kWh) [49]. is the cost ofrunning unit at its minimum power generation [54]. The fol-lowing constraints represent the output power generation limits(8), ramping down/up rate limits (9), (10), minimum ON/OFFtime limits (11), and the relationship between the start-up andshutdown indicators ( and ) (12) of the conventional gen-erating unit [6], [47]–[49], [54]

(8)

(9)

(10)

(11)

(12)


Start-up cost and shut down cost constraints are given as fol-lows [6], [7], [49], [54]:

(13)

(14)

Interested readers can find more details about modeling conven-tional units in [54].

E. Thermal Dynamic Model

A third-order state-space model, which is widely used in lit-erature [11]–[13], [15], is employed to describe the thermal dy-namic model for buildings. This model captures the impacts ofambient temperature and solar irradiance on the indoor temper-ature [12], [13], [15].

(15)

(16)

where is the state vector. is thetemperature of the thermal accumulating layer in the inner wallsand floor in building in time slot and scenario .is the temperature of the envelope of the of building in timeslot and scenario . is the

input control vector with . The coefficientsof matrices and of building can be calculated basedon the effective window area, the fraction of solar irradiationentering the inner walls and floor, and the thermal capacitance,thermal resistance parameters of the building and .Due to the space limitation, interested readers can find moredetails about this building thermal dynamic model in [11], [12].The constraints on the indoor temperature and HVAC powerconsumption are represented as follows:

(17)

(18)

F. Battery Constraints

The constraints (19), (20) capture the limits on the chargingand discharging power as well as the level of energy stored ina battery unit . Here, the level of battery storage at the end ofthe scheduling horizon is equal to its initial energy level. Con-straints (21) are imposed to ensure the battery cannot be chargedand discharged simultaneously in any time slot. The energy dy-namic model for battery is captured in (22).

(19)

(20)

(21)

(22)

G. Involuntary Load Curtailment

Constraints (23) limit the amount of involuntary load cur-tailment at time . The expected amount of involuntary loadcurtailment at time is , while the expected totalnon-HVAC load at time is . In this study, we force

the expected involuntary load curtailment is smaller than a cer-tain percentage of the expected non-HVAC load for every timeslot as described in (24). Constraints (24) can be considered asa reliability criterion for the operation of the MG.

(23)

(24)

H. Renewable Energy Curtailment

The available output power of solar unit at maximum powerpoint (MPP) in time slot and scenario can be calculated basedon the solar irradiance and ambient temperature as follows [5]:

(25)

The output power of wind generator in time slot and sce-nario is given as follows [5]:

if

ifotherwise.

(26)

In each time slot, the amount of wind/solar power curtailmentmust obviously be smaller than the available wind/solar outputpower. Hence, we must have

(27)

(28)

Note that spinning reserve and voluntary demand response loadare not considered in our model; however, their integration intothe model is straightforward.

IV. SOLUTION APPROACH AND COMPUTATION TIME

The power scheduling and bidding problem for joint opti-mization of HVAC systems and distributed resources in the MGdescribed in the previous section is a mixed integer linear pro-gram (MILP), which can be solved effectively by using avail-able commercial solvers such as CPLEX [55]. The absoluteterms in the objective function (1) can be easily transformedinto equivalent linear functions by introducing some auxiliaryvariables [56].Suppose that the forecasts for uncertain parameters in the

considered system model are available. Available forecastingtechniques (e.g., time series, artificial neural networks, supportvector machines) for wind speed, electricity prices, temperature,solar radiation and load [23], [57]–[61] can be used to attain this.In practice, the MG aggregator can obtain forecast data from alocal forecasting center. For simplicity, wind speed, non-HVACload, solar irradiance, ambient temperature, day-ahead and real-time electricity prices are assumed to follow normal distribu-tions where the means are set equal to the forecast values andthe standard deviations are 10%, 3%, 10%, 5%, 5%, and 15% ofthe mean values, respectively. Furthermore, we assume that thesystem uncertainties are independent [53]. Modeling the corre-lation among the uncertain parameters [63]–[65] is beyond thescope of this paper.Based on the distributions of uncertainty parameters, the

Monte Carlo method and Latin Hypercube Sampling techniqueare employed to generate 3000 scenarios with even probability


TABLE ICONVENTIONAL UNIT DATA

(1/3000) where each scenario contains the information of thehourly load, the hourly wind speed, hourly ambient temper-ature, hourly solar irradiance, and the DA and RT electricityprices over the operating day. The fast-forward reductionalgorithm is utilized to reduce the original 3000 scenarios to15 scenarios [50]. In particular, we used GAMS/SCENREDsoftware to run the scenario reduction process [62]. In general,a larger number of scenarios results in higher computation timewhile a small number of scenarios may reduce the accuracyof the results. Considering the tradeoff between computationalcomplexity and modeling accuracy, we decided to choose 15 asthe reasonable number of reduced scenarios. Some sensitivityanalysis has been conducted, which confirms that the variationof the objective function is sufficiently small if larger numberof reduced scenarios is chosen. For brevity, these detailedsensitivity studies are not presented in this paper.All the test cases presented in Section V are implemented on

a desktop computer with 3.5 GHz Intel Core i7-3370 CPU and16 GB RAM. The computational time needed to run scenarioreduction from 3000 scenarios to 15 scenarios using GAMS/SCENRED is recorded to be about 120 seconds. The calculationtime (using CPLEX 12.4) for the proposed model with the 15reduced scenarios is about 1 second, which is pretty small.

V. NUMERICAL RESULTS

We consider a MG whose portfolio consists of three conven-tional generating units, one wind turbine, one solar source, 100buildings with their associated loads, and an optional batteryfacility. The parameters of three conventional units includingtwo microturbines (MT) and one fuel cell (FC) are taken from[5], which are summarized in Table I. For simplicity, the oper-ating cost of each unit is modeled by a single curve segment

[5], [49]. The shutdown cost is assumed to be 10%of the start-up cost. The parameter IC in Table I presents thenumber of hours that a unit is ON (positive) or OFF (negative)at the beginning of the scheduling horizon.We take the building thermal data from [11] and use the

approach in our previous work [12] to model the diversity ofthermal characteristics of buildings. We consider a summercase in this study; however, results for the winter case can beobtained similarly. We consider a 24-hour scheduling periodwhere one time slot is one hour. Unless stated otherwise, wewill set , ; , ; ,; and , .

The forecasts for uncertain parameters in the system modelare assumed to be available. To run the simulation, we usethe historical data for wind speed [66], non-HVAC load [48],solar irradiance [67], ambient temperature [68], day-ahead andreal-time electricity prices [46] with appropriate scaling coef-ficients as in the forecasts. Figs. 1(a), (b), (c) show the hourlyforecasts for the uncertain parameters in the considered model.Wind output power and solar output power can be calculatedfrom the wind speed, solar irradiance, and ambient temperatureby using (25) and (26), respectively. The parameters of thewind and solar sources are retrieved from [5] as follows:• For wind source: , ,

, .• For solar source: and . Understandard condition test (SCT) with ambient temperatureof 25 , solar irradiance of 1000 , and at themaximum power point (MPP) [69], the rated PV power is1100 kW.

System parameters for the base case are set as follows. Thevalue of lost load is set to 1000 $/MWh, the bid devia-tion penalty cost is set to 80 $/MWh, and no penalty costfor renewable power generation curtailment and indoor temper-ature deviation. The maximum involuntary load curtailment isset equal to 5% of the expected non-HVAC load in each time slotand no battery storage unit is included. Also, we do not considerthe maximum power exchange constraints (4). Note that whenwe do not set a limit on the amount of power submitted to theday-ahead market, we need to set sufficiently high to ensurethe bid deviation is not too large and the actual power deliveryis close the the day-ahead schedule.We define the Load Scaling Factor (LSF) as the ratio between

the total forecasted non-HVAC load and the total forecasted re-newable energy generation over the scheduling period. For ex-ample, the LSF in Fig. 1(a) is equal to 0.5, which is chosen inthe base case. For simplicity, we assume that all buildings arealways occupied over the scheduling period. The desired tem-perature is set to 23 and the maximum allowable tempera-ture deviation is set to 2 for all buildings in any time slots.The initial indoor temperatures of all buildings are assumed tobe equal to the desired indoor temperature 23 . HVAC ratedpower in all buildings is set to 10 kW. The data defining thebase case is given in Table II. For all figures presented in thissection, only the system parameters explicitly presented in thefigures are varied, other parameters are the same as in the basecase.Three control schemes are studied in this section as follows:Scheme 1: In this scheme, we apply to the proposed op-timal scheme to the considered MG.Scheme 2: In this scheme, we still apply the proposed op-timal control scheme to the MG; however, the indoor tem-peratures of buildings are always maintained at the set-point. In other word, no temperature deviation is allowed

.Scheme 3 (uncoordinated optimal scheme): In this scheme,HVAC systems and the rest of theMG optimize their powerprofiles separately (Problems 1 and 2 described below).Here, the objective of HVAC scheduling is set to min-imize the operation cost of HVAC systems. HVAC sys-tems submit their aggregated demand bids to the day-ahead


Fig. 1. Wind power, solar power, non-HVAC load, ambient temperature, andprice forecasts. (a) Wind, solar and non-HVAC load forecasts; (b) Hourly fore-casted day-ahead and real-time electricity prices; (c) Hourly forecasted ambienttemperature.

TABLE IISYSTEM PARAMETERS IN THE BASE CASE

market and face the same penalty scheme for bid deviationcharge as we described above. The technical constraintsfor HVAC system, thermal constraints for buildings, andothers remain the same. The only the difference is that thepower balancing equation (29) does not have the HVAC-re-lated terms.

Problem 1: We aim to minimize the expected operating costof HVAC systems as follows:

and other constraints for HVAC system and thermal comfort re-quirement (15), (16), (17), and (18). Here, and arepositive numbers which denote the imported power for HVACsystems.Problem 2: For this problem, the expected profit for the MG

is maximized. The objective function remains the same as (1)but the discomfort cost term is not included. The power balanceequation now becomes

and other constraints for the components in the MG are un-changed as described in the problem formulation.

A. Comparison Between Scheme 1 and Scheme 2

Fig. 2(a), 2(b) illustrate the advantages of the proposed op-timal scheme, which exploits the flexibility offered by buildingthermal storage capacity, and the flexible comfort requirements(Scheme 1) compared to the case where no temperature devi-ation is allowed (Scheme 2 with ). As discussed inSection I, the curtailment of renewable energy generation is re-quired in some cases to avoid the high penalty charge on biddeviation and to ensure that the real time power delivery is suf-ficiently close to the day-ahead schedule. Due to their flexibility,the HVAC systems could increase their power consumption byabsorbing more energy from renewable sources to help the MGreduce the amount of renewable energy curtailment.Fig. 2(a) confirms that the amount of renewable energy cur-

tailment is reduced as increases. Furthermore, the increasein discomfort penalty cost results in more curtailed renewableenergy. Fig. 2(b) shows the expected profit (i.e., the value of theobjective function) for different values of and . Asevident, as increases, theMG expected profit increases. Also,as the cost of temperaturedeviation increases, theMGexpectedprofit decreases. In fact, largervaluesof (and/or smallervaluesof ) enables more flexible scheduling of the HVAC power con-sumption, which results in larger performance gain in terms ofboth MG profit and renewable energy curtailment reduction.

B. Comparison Between Scheme 1 and Scheme 3

Fig. 3(a), 3(b), and 3(c) show the advantages of the coordi-nated optimal scheme compared to the uncoordinated schemeversus the curtailment parameter . We compare the two


Fig. 2. Impacts of and on the optimal solution. (a) Renewable energycurtailment; (b) Expected profit.

schemes in two cases with and without battery. For the case withbattery, one battery unit with capacity of 200 kWh is chosenwhere the charging/discharging power ratings are set equal to100 kW. The minimum and maximum energy stored in the bat-tery are 40 kWh and 180 kWh, respectively. Table III summa-rizes the parameters of the considered battery unit. We can seethat the total amount of renewable energy curtailment is muchsmaller in the coordinated scheme compared with that of the un-coordinated one. This is because in the uncoordinated scheme,we do not exploit the flexibility offered by HVAC systems toabsorb the fluctuation of renewable energy generation.To mitigate the high penalty due to the bid deviation charge,

some surplus renewable energy needs to be curtailed to en-sure that the real-time power delivery is close to the day-aheadschedule. However, in the coordinated scheme, HVAC systemscan increase their power consumption when the renewable en-ergy sources produce surplus energy, which helps reduce theamount of renewable energy curtailment. Additionally, it canbe observed that the amount of renewable energy curtailmentdecreases as increases and it tends to zeros as be-comes larger. Fig. 3(b) shows that the bid deviation charges forthe uncoordinated scheme ismuch higher than that in the coordi-nated scheme. This is because when the renewable energy gen-eration is smaller than expected, in the coordinated scheme, wecan reduce the power consumption of HVAC systems to reducethe charge due to the shortage of delivered power to the marketas being scheduled in advance. Finally, the expected profit forthe MG is also higher in the coordinated scheme than the one inthe uncoordinated scheme as shown in Fig. 3(c).

Fig. 3. Comparison between coordinated and uncoordinated schemes. (a) Re-newable energy curtailment; (b) Expected bid deviation charge; (c) Expectedprofit.

TABLE IIIBATTERY PARAMETERS

C. Sensitivity Analysis

We now investigate the impacts of various design and systemparameters on the optimal solution.Fig. 4(a) and 4(b) illustrate the impacts of temperature devia-

tion penalty cost on the optimal solution. Specifically, Fig. 4(a)


Fig. 4. Impact of temperature deviation penalty on the optimal solution.(a) Renewable energy curtailment; (b) Expected profit.

confirms that the energy curtailment tends to increase as in-creases. This is due to the fact that as increases, the indoortemperature is forced to be closer to the desired value toreduce the climate discomfort cost, which means we have theless flexibility in controlling the HVAC power consumption.Moreover, the amount of renewable energy curtailment becomessaturated at certain values of where the indoor temperatureof all buildings becomes very close to the desired temperature.Also,we can see that the expected profit of theMGdecreases andbecomesflattenedas is sufficiently large as shown inFig. 4(b).In addition, as parameter increases, we expect that the

bid deviation becomes smaller to avoid the high bid deviationpenalty cost, which results in less flexibility in controlling theoperation of the MG. Therefore, the expected profit for theMG decreases and the amount of renewable energy curtailmentincreases as increases, which is confirmed by the results inFigs. 4(a), 4(b), 5(a), and 5(b).Fig. 6(a), 6(b) illustrate the variation of the amount of total re-

newable energy curtailment and the MG expected profit versusthe HVAC rated power. This figure shows that lower amount ofrenewable energy curtailment and higher MG expected profitcan be achieved as the HVAC rated power increases, whichindeed offers more flexibility in controlling the HVAC powerconsumption. However, with each value of battery capacity, thequantities are saturated at certain values of HVAC rated power,which can be interpreted as follows. The HVAC power con-sumption can only be varied within a certain range to meet theindoor temperature comfort requirement. Here, the minimumand maximum energy levels stored in the battery are set equal to20% and 90% of the battery capacity. The maximum charging/discharging rate of battery is set equal to 100 kW.



The impact of the maximum allowable power exchangebetween the MG and the main grid on the optimal


Fig. 7. Impact of on the optimal solution. (a) Renewable energy cur-tailment; (b) Expected profit.

solution is presented in Fig. 7(a) and 7(b). In particular,Fig. 7(a) shows that the amount of renewable energy curtail-ment increases for decreasing . This can be interpretedas follows. If is small and the amount of availablerenewable energy is large, then the HVAC systems may notbe able to absorb all the surplus renewable energy due to thetemperature comfort constraint, and directly affects theability of exchange power between the MG and the main grid.Therefore, more power curtailment is expected as issmall. Also, the parameter has a direct impact on theability of the MG in offering bid to the power market; therefore,the expected profit of the MG increases before getting saturatedas increases as being shown in Fig. 7(b).The variations in expected profit of the MG with different

values of the LSF and are presented in Fig. 8(a). Here, thenegative value of expected profit corresponds to the case wheretheMGneeds topurchaseadditional energy fromthemaingridonaverage; in otherwords, theMGhas to pay themain grid operatorfor its operation. This is the case when the local load consumesmore energy than what can be generated by the local renewableenergy sources. The deficit amount of energy must, therefore, becompensated by importing energy from the main grid. Note alsothat as the LSF is sufficiently high, the MG may need to operateits local conventional generation units due to the constraints onthemaximumamountof importedpower.The conventional unitsin the considered model are only needed for backup purposesbecause their operation cost is relatively high, which impliesthat importing energy from the grid might be more cost-efficientthan running conventional units to serve the local demand. Theoptimal bid quantities submitted to the day-ahead market fordifferent values of the LSF are shown in Fig. 8(b). Here, if thepowerbid is negative, theMGimports power from themaingrid.

Fig. 8. Impacts of and LSF on the optimal solution. (a) Expected profit;(b) Day-ahead hourly bids.

Fig. 9. Impact of uncertainty level on the expected optimal profit.

To investigate the impact of the uncertainty level on the op-timal solution, we utilize the uncertainty scaling factor (USF)where the base case described in Section IV has . Also,we scale the standard deviations of uncertain parameters in thebase case by the factor of USF to obtain the result presented inFig. 9. It can be observed that the MG expected profit decreasesas USF increases (i.e., the uncertainty level increases).Finally, we show the impact of battery operation cost (degra-

dation) parameter on the gain as battery storage is utilized.The presented gain captures the difference between the expectedprofit when using the battery and when not using the battery. Itcan be observed from Fig. 10 that the gain due to utilizing bat-tery storage facility decreases and becomes saturated as in-creases. This can be interpreted as follows. If is sufficientlyhigh, the cost saving due to energy storage can be neutralized bythe battery degradation (wear) cost. In general, if is smallthen utilization of battery storage can result in positive perfor-mance gain.


Fig. 10. Impacts of battery charging and discharging (degradation) cost.

VI. CONCLUSION

In this paper, we have proposed an optimal power schedulingframework for a MG with renewable energy considering users’thermal comfort requirements and other system constraints.Extensive numerical results have been presented to illustratethe great benefits of our design in reducing the renewableenergy curtailment, mitigating the high penalty due to energyimbalance, and increasing the expected profit for the MG byexploiting the building thermal dynamics. Based on thesenumerical studies, the following conclusions are in order.1) Coordination of HVAC load (or in general flexible loads)and RESs through a unified energy management frame-work is important. Integrating flexible HVAC load sched-uling into energy management decisions of the MG aggre-gator can increase significantly its expected profit and re-duce the amount of renewable energy curtailment, whichalso helps avoid the high energy imbalance charge causedby bid deviation.

2) The benefits of the proposed coordinated scheme dependon the flexibility offered by theHVAC system. Specifically,the expected profit of the MG aggregator increases and theamount of renewable energy curtailment decreases as themaximum allowable temperature deviation increases,the cost of temperature deviation decreases, and the ratedpower of HVAC systems increases. However, the perfor-mance gain becomes saturated at certain values of , ,and the HVAC rated power.

3) Cost of bid deviation and cost of renewable energycurtailment have significant impacts on the optimalsolution. In particular, the MG expected profit decreasesand the amount of renewable energy curtailment increasesas increases and/or increases.

4) Battery storage can help the MG aggregator reduce theamount of renewable energy curtailment and increase theexpected profit. The expected profit of the MG aggregatorincreases and the amount renewable energy curtailmentdecreases as the maximum power exchange limit betweenthe MG aggregator and the main grid increases.However, it is saturated as becomes sufficientlylarge. Finally, the uncertainty level has significant impactson the optimal solution.

REFERENCES[1] M. E. Khodayar and M. Shahidehpour, “Stochastic price-based coordi-

nation of intrahour wind energy and storage in a generation company,”IEEE Trans. Sustain. Energy, vol. 4, no. 3, pp. 554–562, Jul. 2013.

[2] J. G. Gonzalez, R. M. R. de la Muela, L. M. Santos, and A. M. Gon-zalez, “Stochastic joint optimization of wind generation and pumped-storage units in an electricity market,” IEEE Trans. Power Syst., vol.23, no. 2, pp. 460–468, May 2008.

[3] Q. Wang, J. Wang, and Y. Guan, “Price-based unit commitment withwind power utilization constraints,” IEEE Trans. Power Syst., vol. 28,no. 3, pp. 2718–2726, Aug. 2013.

[4] M. E. Khodayar, M. Shahidehpour, and L. Wu, “Enhancing the dis-patchability of variable wind generation by coordination with pumped-storage hydro units in stochastic power systems,” IEEE Trans. PowerSyst., vol. 28, no. 3, pp. 2808–2818, Aug. 2013.

[5] S. X. Chen, H. B. Gooi, and M. Q. Wang, “Sizing of energy storagefor microgrids,” IEEE Trans. Smart Grid, vol. 1, no. 4, pp. 1997–2006,Mar. 2012.

[6] S. Bahramirad, W. Reder, and A. Khodaei, “Reliability-constrainedoptimal sizing of energy storage system in a microgrid,” IEEE Trans.Smart Grid, vol. 3, no. 4, pp. 2056–2062, Dec. 2012.

[7] M. E. Khodayar, W. Lei Wu, and M. Shahidehpour, “Hourly coordi-nation of electric vehicle operation and volatile wind power generationin SCUC,” IEEE Trans. Smart Grid, vol. 3, no. 3, pp. 1271–1279, Sep.2012.

[8] C. Liu, J. Wang, A. Botterud, Y. Zhou, and A. Vyas, “Assessment ofimpacts of PHEV charging patterns on wind-thermal scheduling by sto-chastic unit commitment,” IEEE Trans. Smart Grid, vol. 3, no. 2, pp.675–683, Jun. 2012.

[9] D. J. Swider, “Compressed air energy storage in an electricity systemwith significant wind power generation,” IEEE Trans. Energy Con-vers., vol. 22, no. 1, pp. 95–102, Mar. 2007.

[10] S. Kamalinia and M. Shahidehpour, “Generation expansion planningin wind-thermal power systems,” IET Trans. Gener, Transm., Distrib.,vol. 4, no. 8, pp. 940–951, Aug. 2010.

[11] A. Thavlov, “Dynamic optimization of power consumption,” M.S.thesis, Tech. Univ. Denmark, Kongens Lyngby, Denmark, 2008.

[12] D. T. Nguyen and L. B. Le, “Joint optimization of electric vehicle andhome energy scheduling considering user comfort preference,” IEEETrans. Smart Grid, vol. 5, no. 1, pp. 188–199, Jan. 2014.

[13] Y. Zong, D. Kullmann, A. Thavlov, O. Gehrke, and H. W. Bindner,“Application of model predictive control for active load managementin a distributed power systemwith high wind penetration,” IEEE Trans.Smart Grid, vol. 3, no. 2, pp. 1055–1062, Jun. 2012.

[14] H. Nguyen, D. T. Nguyen, and L. B. Le, “Home energy managementwith generic thermal dynamics and user temperature preference,” inProc. IEEE SmartGridCom, Vancouver, BC, Canada, Oct. 2013.

[15] R. Halvgaard, N. K. Poulsen, H. Madsen, H. , and J. B. Jorgensen,“Economic model predictive control for building climate control in asmart grid,” in Proc. IEEE PES Innov. Smart Grid Technol. (ISGT),Washington, DC, USA, Jan. 2012.

[16] U.S. Environmental Protection Agency [Online]. Available: www.epa.gov/greenbuilding/pubs/gbstats.pdf

[17] A. A. Thatte, L. Xie, D. E. Viassolo, and S. Singh, “Risk measure basedrobust bidding strategy for arbitrage using a wind farm and energystorage,” IEEE Trans. Smart Grid, to be published.

[18] X. Guan, Y. C. Ho, and F. Lai, “An ordinal optimization based biddingstrategy for electric power suppliers in the daily energy market,” IEEETrans. Power Syst., vol. 16, no. 4, pp. 788–797, Nov. 2001.

[19] H. Song, C. C. Liu, J. Lawarrée, and R. W. Dahlgren, “Optimalelectricity supply bidding by Markov decision process,” IEEE Trans.Power Syst., vol. 15, no. 2, pp. 618–624, May 2000.

[20] T. Li and S. M. Shahidehpour, “Strategic bidding of transmission-con-strained GENCOs with incomplete information,” IEEE Trans. PowerSyst., vol. 20, no. 1, pp. 437–447, Feb. 2005.

[21] V. P. Gountis and A. G. Bakirtzis, “Bidding strategies for electricityproducers in a competitive electricity marketplace,” IEEE Trans.Power Syst., vol. 19, no. 1, pp. 356–365, Feb. 2004.

[22] A. Botterud, Z. Zhou, J. Wang, R. J. Bessa, H. Keko, J. Sumaili, andV. Miranda, “Wind power trading under uncertainty in LMP markets,”IEEE Trans. Power Syst., vol. 27, no. 2, pp. 894–903, May 2012.

[23] M. Shahidehpour, H. Yamin, and Z. Li, Market Operations in Elec-tric Power Systems: Forecasting, Scheduling, and Risk. New York:Wiley-IEEE Press, 2002.

[24] M. Carrin, A. B. Philpott, A. J. Conejo, and J. M. Arroyo, “A stochasticprogramming approach to electric energy procurement for large con-sumers,” IEEE Trans. Power Syst., vol. 22, no. 2, pp. 744–754, May2007.

[25] A. Safdarian, M. Fotuhi-Firuzabad, and M. Lehtonen, “A stochasticframework for short-term operation of a distribution company,” IEEETrans. Power Syst., vol. 28, no. 4, pp. 4712–4721, Nov. 2013.

[26] R. Palma-Behnke, A. J. L. Cerda, L. S. Vargas, and A. Jofre, “A dis-tribution company energy acquisition market model with integrationof distributed generation and load curtailment options,” IEEE Trans.Power Syst., vol. 20, no. 4, pp. 1718–1727, Nov. 2005.

[27] A. Hatami, H. Seifi, and M. K. Sheikh-el-Eslami, “A stochastic-baseddecision-making framework for an electricity retailer: Time-of-usepricing and electricity portfolio optimization,” IEEE Trans. PowerSyst., vol. 26, no. 4, pp. 1808–1816, Nov. 2011.


[28] Y. Zheng, Z. Y. Dong, F. J. Luo, K.Meng, J. Qiu, and K. P.Wong, “Op-timal allocation of energy storage system for risk mitigation of DISCOswith high renewable penetrations,” IEEE Trans. Power Syst., to be pub-lished.

[29] S. I. Vagropoulos and A. G. Bakirtzis, “Optimal bidding strategy forelectric vehicle aggregators in electricity markets,” IEEE Trans. PowerSyst., to be published.

[30] R. J. Bessa, M. A. Matos, F. J. Soares, and J. A. P. Lopes, “Optimizedbidding of a EV aggregation agent in the electricity market,” IEEETrans. Smart Grid, vol. 3, no. 1, pp. 443–452, Mar. 2012.

[31] A. G. Tsikalakis and N. D. Hatziargyriou, “Centralized control for op-timizing microgrids operation,” IEEE Trans. Energy Convers., vol. 23,no. 1, pp. 241–248, Mar. 2008.

[32] S. Grijalva and M. U. Tariq, “Prosumer-based smart grid architectureenables a flat, sustainable electricity industry,” in Proc. IEEE PESInnov. Smart Grid Technol. (ISGT), Jan. 17–19, 2011, pp. 1–6.

[33] H. Pandi, J. M. Morales, A. J. Conejo, and I. Kuzle, “Offering modelfor a virtual power plant based on stochastic programming,” J. Appl.Energy, vol. 105, pp. 282–292, May 2013.

[34] S. Y. Derakhshandeh, A. S. Masoum, S. Deilami, M. A. S. Masoum,and M. E. Hamedani Golshan, “Coordination of generation schedulingwith PEVs charging in industrial microgrids,” IEEE Trans. PowerSyst., vol. 28, no. 3, pp. 3451–3461, Aug. 2013.

[35] T. Logenthiran, D. Srinivasan, A. M. Khambadkone, and H. N. Aung,“Multiagent system for real-time operation of a microgrid in real-timedigital simulator,” IEEE Trans. Smart Grid, vol. 3, no. 2, pp. 925–933,Jun. 2012.

[36] T. Logenthiran, D. Srinivasan, and A. M. Khambadkone, “Multi-agentsystem for energy resource scheduling of integrated microgrids in adistributed system,” J. Electr. Power Syst. Res., vol. 81, no. 1, pp.138–148, Jan. 2011.

[37] C. Chen, S. Duan, T. Cai, B. Liu, and G. Hu, “Smart energy manage-ment system for optimal microgrid economic operation,” IET Trans.Renew. Power7 Gen., vol. 5, no. 3, pp. 258–267, May 2011.

[38] E. Mashhour and S. M. Moghaddas-Tafreshi, “Bidding strategy of vir-tual power plant for participating in energy and spinning reserve mar-ketspart I: Problem formulation,” IEEE Trans. Power Syst., vol. 26, no.2, pp. 949–956, May 2011.

[39] S. Kahrobaee, R. A. Rajabzadeh, L. K. Soh, and S. Asgarpoor, “A mul-tiagent modeling and investigation of smart homes with power gener-ation, storage, and trading features,” IEEE Trans. Smart Grid, vol. 4,no. 2, pp. 659–668, Jun. 2013.

[40] D. T. Nguyen and L. B. Le, “Optimal energy management for coop-erative microgrids with renewable energy resources,” in Proc. IEEESmartGridCom, Vancouver, BC, Canada, Oct. 2013.

[41] H. S. V. S. K. Nunna and S. Doolla, “Demand response in smart dis-tribution system with multiple microgrids,” IEEE Trans. Smart Grid,vol. 3, no. 4, pp. 1641–1649, Dec. 2012.

[42] G. Celli, F. Pilo, G. Pisano, and G. G. Soma, “Optimal participationof a microgrid to the energy market with an intelligent EMS,” in Proc.IEEE Power Eng. Conf. (IPEC), Singapore, Nov. 29–Dec. 2 2005.

[43] A. Bagherian and S.M.M. Tafreshi, “A developed energy managementsystem for a microgrid in the competitive electricity market,” in Proc.IEEE PowerTech, Bucharest, Romania, Jun. 28–Jul. 2 2009.

[44] M. E. Khodayar, M. Barati, and M. Shahidehpour, “Integration of highreliability distribution system in microgrid operation,” IEEE Trans.Smart Grid, vol. 3, no. 4, pp. 1997–2006, Dec. 2012.

[45] Community Power Network [Online]. Available: http://community-powernetwork.com/

[46] PJM—Markets and operations [Online]. Available: http://pjm.com/markets-and-operations.aspx

[47] W. Lei, M. Shahidehpour, and L. Tao, “Stochastic security-con-strained unit commitment,” IEEE Trans. Power Syst., vol. 22, no. 2,pp. 800–811, May 2007.

[48] J. Wang, M. Shahidehpour, and L. Zuyi, “Security-constrained unitcommitment with volatile wind power generation,” IEEE Trans. PowerSyst., vol. 23, no. 3, pp. 1319–1327, Aug. 2008.

[49] J. M.Morales, A. J. Conejo, and J. Perez-Ruiz, “Economic valuation ofreserves in power systems with high penetration of wind power,” IEEETrans. Power Syst., vol. 24, no. 2, pp. 900–910, May 2009.

[50] J. Dupacová, N. Growe-Kuska, and W. Romisch, “Scenario reductionin stochastic programming: An approach using probability metrics,”Math. Program., pp. 493–511, 2003.

[51] W. Kempton and J. Tomic, “Vehicle-to-grid power fundamentals: Cal-culating capacity and net revenue,” J. Power Sources, vol. 144, no. 1,pp. 268–279, Jun. 2005.

[52] M. D. Hopkins, A. Pahwa, and T. Easton, “Intelligent dispatch for dis-tributed renewable resources,” IEEE Trans. Smart Grid, vol. 3, no. 2,pp. 1047–1054, Jun. 2012.

[53] C. Sahin, M. Shahidehpour, and I. Erkmen, “Allocation of hourly re-serve versus demand response for security-constrained scheduling ofstochastic wind energy,” IEEE Trans. Sustain. Energy, vol. 4, no. 1,pp. 219–228, Jan. 2013.

[54] M. Carrion and J. M. Arroyo, “A computationally efficient mixed-in-teger linear formulation for the thermal unit commitment problem,”IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1371–1378, Aug. 2006.

[55] CPLEX Solver [Online]. Available: http://www-01.ibm.com/software/websphere/ilog/

[56] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge,U.K.: Cambridge Univ. Press, 2004.

[57] F. J. Nogales, J. Contreras, A. J. Conejo, and R. Espinola, “Forecastingnext-day electricity prices by time series models,” IEEE Trans. PowerSyst., vol. 17, pp. 342–348, May 2002.

[58] H. S. Hippert, C. E. Pedreira, and R. C. Souza, “Neural networks forshort-term load forecasting: A review and evaluation,” IEEE Trans.Power Syst., vol. 16, no. 1, pp. 44–55, Feb. 2001.

[59] M. Lei, L. Shiyan, J. Chuanwen, L. Hongling, and Z. Yan, “A review onthe forecasting of wind speed and generated power,” Renew. Sustain.Energy Rev., vol. 13, no. 4, pp. 915–920, May 2009.

[60] S. M. Chen and J. R. Hwang, “Temperature prediction using fuzzy timeseries,” IEEE Trans. Syst. Man. Cybern. A, vol. 30, no. 2, pp. 263–275,Apr. 2000.

[61] A. J. Conejo, M. Carrion, and J. M. Morales, “Decision Making UnderUncertainty in Electricity Markets,” in International Series in Opera-tions Research & Management Science. New York: Springer, 2010.

[62] GAMS/SCENRED Documentation [Online]. Available: http://www.gams.com/docs/document.htm

[63] J. M. Morales, S. Pineda, A. J. Conejo, and M. Carrión, “Scenario re-duction for futures market trading in electricity markets,” IEEE Trans.Power Syst., vol. 24, no. 2, pp. 878–888, May 2009.

[64] J. M. Morales, R. Mnguez, and A. J. Conejo, “A methodology to gen-erate statistically dependent wind speed scenarios,” J. Appl. Energy,vol. 87, no. 3, pp. 843–855, Mar. 2010.

[65] L. Baringo and A. J. Conejo, “Correlated wind-power production andelectric load scenarios for investment decisions,” J. Appl. Energy, vol.101, pp. 475–482, Jan. 2013.

[66] NWTC M2 Tower [Online]. Available: http://www.nrel.gov/midc/nwtc_m2/

[67] National Solar Radiation Data Base: 1991–2010 update [Online].Available: http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2010

[68] Weather Underground [Online]. Available: http://www.wunderground.com/

[69] Y. Riffonneau, S. Bacha, F. Barruel, and S. Ploix, “Optimal powerflowmanagement for grid connected PV systemswith batteries,” IEEE.Trans. Sustain. Energy, vol. 2, no. 3, pp. 309–320, Jul. 2011.

Duong Tung Nguyen received the B.Eng. fromHanoi University of Technology, Vietnam, in 2011.He is currently a graduate student at the InstitutNational de la Recherche Scientifique (INRS),Université du Québec, Montréal, QC, Canada. Hisresearch lies in the areas of smart grids and powersystem economics with current focus on control andoptimization issues for microgrids.

Long Bao Le (S’04–M’07–SM’12) received theB.Eng. (with Highest Distinction) degree from HoChi Minh City University of Technology, Vietnam,in 1999, the M.Eng. degree from Asian Institute ofTechnology, Pathumthani, Thailand, in 2002, andthe Ph.D. degree from the University of Manitoba,Winnipeg, MB, Canada, in 2007.From 2008 to 2010, he was a Postdoctoral Re-

search Associate with Massachusetts Institute ofTechnology, Cambridge, MA, USA. Since 2010,he has been an assistant professor with the Institut

National de la Recherche Scientifique (INRS), Université du Québec, Montréal,QC, Canada. His current research interests include smartgrids, cognitive radioand dynamic spectrum sharing, radio resource management, network controland optimization for wireless networks. He is a co-author of the book RadioResource Management in Multi-Tier Cellular Wireless Networks (Wiley, 2013).Dr. Le is a member of the editorial board of IEEE Communications Surveys

and Tutorials and IEEE Wireless Communications Letters. He has served astechnical program committee co-chairs of the Wireless Access track at IEEEVTC2014-Fall, Wireless Networks track at IEEE VTC2011-Fall, and the Cog-nitive Radio and Spectrum Management track at IEEE PIMRC2011.

! Cassidy Morgan Tits !

Documents

Transcript of ! Cassidy Morgan Tits !